CN111079075B - Non-2-base DFT optimized signal processing method - Google Patents
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Abstract
The invention belongs to the field of digital signal processing, optimizes a Cooley-Tukey algorithm based on non-2-base DFT, and discloses a signal processing method optimized by non-2-base DFT, which optimizes the prime factor decomposition of the Cooley-Tukey algorithm, disassembles N-point DFT according to the prime factor decomposition, and processes signals by using the Cooley-Tukey algorithm on the basis. The invention improves the reliability of signal processing and the accuracy of fixed-point calculation processing, and reduces the difficulty of signal processing of fixed-point non-2-base N-point DFT.
Description
Technical Field
The invention belongs to the field of digital signal processing, and relates to a non-2-base DFT optimized signal processing method in a 5G system, which is mainly used for carrying out engineering optimization aiming at a non-2-base N-point DFT quality factor decomposition algorithm in digital signal processing. The fixed-point processing of the DSP is facilitated, the development difficulty of the non-2-base N-point DFT is reduced, and certain universality and universality are achieved.
Background
In a 5G mobile communication system, in order to satisfy the physical layer design performance of the system, fixed point DFT is widely used in the process of digital signal processing. For example, when processing Sounding signals, the signal length is 273, and non-2-base DFT processing is required. The 2-base DFT can be directly realized by adopting a very mature FFT algorithm. While there are roughly two implementations of DFT for non-2-base N-points: a method includes the steps that N points are interpolated to obtain an M point of a base 2, FFT of the M point is achieved through the base-2 or the base-4, and then non-2-base N point DFT is obtained through down sampling; secondly, the N is subjected to Prime factor decomposition, and the DFT of each Prime factor point is calculated in an iterative manner to obtain the DFT of the N point, wherein a Prime-factor FFT algorithm (PFA) and a Cooley-Tukey algorithm are two algorithms which are frequently used at present. The principle of the coprime factor algorithm, also known as Good-Thomas algorithm, is to convert an N-point DFT into a two-dimensional DFT of size N1 × N2, and then continue to recursively use PFA for N1 (or N2) until it cannot be decomposed. The disadvantage of the PFA algorithm is that N1 and N2 are required to be relatively prime, so when factoring the prime factor for N, the PFA algorithm cannot be applied if there is a prime factor power in the factorization result. The Cooley-Tukey algorithm is formed by a mixed-radix algorithm, the Cooley-Tukey algorithm is the same as the PFA algorithm and also converts an N point DFT into a two-dimensional DFT with the size of N1 multiplied by N2, and then iteration is carried out on the DFT, although the calculation steps are more than that of the PFA algorithm, the multiplication procedure of the PFA algorithm is multiplied by Twiddle factors, but different from the PFA algorithm, N1 and N2 of the Cooley-Tukey algorithm do not need to be coprime, so that the algorithm has good universality. When the Cooley-Tukey algorithm is used for realizing DFT calculation, particularly fixed-point DFT calculation, the whole process from decomposition of prime factors to DFT calibration compensation is complex to develop, and calibration accuracy cannot be guaranteed.
Disclosure of Invention
The invention aims to provide a non-2-base DFT optimized signal processing method, which improves the reliability of signal processing and the accuracy of fixed-point calculation processing and reduces the difficulty of signal processing of fixed-point non-2-base N-point DFT.
The invention provides a non-2-base DFT optimized signal processing method, which is based on a Cooley-Tukey algorithm, optimizes the prime factor decomposition of the Cooley-Tukey algorithm, decomposes N-point DFT according to the prime factor decomposition, and processes signals by using the Cooley-Tukey algorithm on the basis; the quality factor decomposition specifically comprises the following steps: for a fixed-point non-2-basis signal of length N, prime factorize N, N = N 1 ×N 2 ×…×N i In which N is m Are prime numbers and can be repeated, and m belongs to {1,2, \8230;, i }; the N-point DFT disassembly method specifically comprises the following steps: all N are m In descending order, the sequence is { N' 1 ，N′ 2 ，…，N′ i Are combined into N' 2 N′ 3 …N′ i ×N′ 1 ，N′ 3 N′ 4 …N′ i ×N′ 2 ，N′ 4 N′ 5 …N′ i ×N′ 3 ，…，N′ i ×N′ i-1 Divided into i-1 matrices.
DFT (discrete Fourier transform) factors need to be calculated when the Cooley-Tukey algorithm processes signalsAnd adjusting the calculation of the DFT factor and the Twdle factor after the prime factor decomposition optimization of the seed factor and the Twdle factor, specifically, calculating the DFT factor: decomposing the DFT with N points, and collecting the arranged factors according to the arranged factors { N' 1 ，N′ 2 ，…，N′ i Generating a DFT factor, and scaling the DFT factor; computing Twiddle factor: and on the basis of disassembling the N-point DFT, generating a Twdle factor according to the divided matrix, and calibrating the Twdle factor.
The invention also comprises calculating scaling compensation, wherein the scaling compensation is used for measuring and calculating actual signal power usage, and factors are combined into { N 'on the basis of decomposing N-point DFT' 1 ，N′ 2 ，…，N′ i And (4) carrying out calibration backspacing value compensation calculation: b = ([ log) 2 N′ 1 ]+[log 2 N′ 2 ]+…+[log 2 N′ i ]) X r, where B is the number of scaled compensation bits and r is the number of scaled integer bits.
The invention specifically processes the signals as follows: (1) For N of m < i m Point DFT, divide the signal into N' m+1 N′ m+2 …×N′ i Groups, each group is respectively multiplied and added with the mth group DFT factor to be calculated as N m Outputting a point DFT; n' m+1 N′ m+2 …×N′ i Group N m The outputs of the point DFTs are multiplied by the m-th group Twdle factors, and the result is N' m+1 N′ m+2 …×N′ i Input of point DFT, wherein when m =1, the signal refers to the fixed-point non-2-base signal of the original input, and the rest refers to N m-1 The result of multiplying the output of the point DFT by the (m-1) th set of Twdle factors; (2) performing step i-1 of step (1); (3) Calculating N' i And (3) point DFT: is N' i-1 The result of multiplying the point DFT by the corresponding Twdle factor is iterated N 'from the inner layer to the outer layer, respectively' i-1 ，N′ i-2 ，…N′ 2 Calculating N 'again' i Point DFT; (4) To N' i And the output of the point DFT is output after being rearranged in sequence.
The invention has the following beneficial effects: on the basis of the original Cooley-Tukey algorithm, the invention optimizes and improves the processes of decomposing the quality factor, decomposing the DFT at N points, calculating the DFT factor, calculating the Twidle factor, calculating the calibration compensation and the like. The automation of the processes of decomposing prime factors, disassembling N-point DFTs, calculating DFT factors, calculating Twidle factors, calculating calibration compensation and the like is realized by optimizing the algorithm, so that the original complicated and complicated calculation process is simplified, and the difficulty of signal processing of non-2-base DFTs is reduced; meanwhile, the invention can modify calibration according to different requirements, calculate and feed back calibration compensation results, and ensure the precision of signal processing; and after optimization, the Cooley-Tukey algorithm iterative operation is conveniently realized in a modularized manner, the reliability of signal processing is improved, and the method is applicable to any non-2-base DFT or IDFT.
Drawings
FIG. 1 is a schematic diagram of a calculation process for factorization of prime factors, DFT factors, twdle factors, and scaling compensation;
FIG. 2 is a schematic diagram of a first-step splitting implementation of a 273-point DFT algorithm;
FIG. 3 is a schematic diagram of a second-step implementation of a 273-point DFT algorithm;
FIG. 4 is a 273 point DFT algorithm data processing map;
FIG. 5 is a flow chart of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention clearer and more obvious, the present invention is further described in detail below with reference to the accompanying drawings and technical solutions.
The invention is further improved on the basis of the Cooley Tukey algorithm, and is favorable for realizing modularization. As shown in fig. 5, the method includes decomposing prime factors and scaling, performing DFT split calculation and sequence rearrangement.
As shown in fig. 1, in the prime factor decomposition and scaling process, the prime factor decomposition is performed on the non-2-base time domain sequence to be subjected to DFT calculation, N-point DFT is disassembled, DFT factors are calculated, twiddle factors are calculated, and scaling compensation is calculated. The optimized processing flows can be realized by software. These processes only need to take the non-2-base time domain sequence length N as input and output DFT factor, twiddle factor, prime factor (including repeated factor) and scaling compensation. Wherein, the DFT factor and the Twdle factor have no precedence requirement. The DFT factor and the Twdle factor are used for calculation, the prime factor determines a non-2-base time domain sequence splitting structure, and the scaling compensation is used for calculating the actual signal power.
Decomposition quality factor: performing prime factorization on the DFT sequence length N, recording all factors so as to be used for disassembling the N-point DFT process, recording the number of the factors as i, and determining the number of times of iterative computation required by the N-point DFT according to the number of the factors; n = N 1 ×N 2 ×…×N i In which N is m Are all prime numbers and can be repeated, m ∈ {1,2, \ 8230;, i }.
Disassembling N-point DFT: based on the decomposition quality factor, all the factors N m In descending order, the sequence is { N' 1 ，N′ 2 ，…，N′ i }, combining the factors to be N' 2 N′ 3 …N′ i ×N′ 1 ，N′ 3 N′ 4 …N′ i ×N′ 2 ，N′ 4 N′ 5 …N′ i ×N′ 3 ，…，N′ i ×N′ i-1 And dividing the matrix into i-1 matrixes so as to calculate the Twdle factor, calculating the DFT and using the Twdle factor multiplication process.
Calculating a DFT factor: the method is based on the N-point DFT, and comprises the steps of generating DFT factors according to the arranged factor sets and calibrating the DFT factors. For i factors, the DFT factor is calculated i times.
Computing Twiddle factor: and on the basis of the N-point DFT, generating a Twdle factor according to the divided matrix, and calibrating the Twdle factor. For the i factors, the Twdle factor is calculated i-1 times.
Calculating a scaling compensation: establishing a factor set { N 'obtained by disassembling and arranging on the basis of disassembling N-point DFT' 1 ，N′ 2 ，…，N′ i And (4) carrying out calibration backspacing value compensation calculation:
where B is the scaling compensation bit number, r is the integer scaling bit number, and for a DFT scaling value Q (a, B), r = a-B, where a is the scaling bit number of the floating point number, and B is the fractional bit number of the scaling number. The scaling compensation B of the N-point DFT can be obtained by the formula calculation.
With reference to fig. 2, 3, 4 and 5, taking DFT of a full bandwidth 273PRB in a 5G system as an example, the DFT is performed to perform DFT splitting calculation and sequence rearrangement. 273 dividing the prime factor to obtain 13 × 7 × 3 (already sorted from large to small, let N be 1 ＝13，N 2 ＝7，N 3 = 3), so the 273 point DFT is split into three steps: the first step is to calculate 13-point DFT and multiply the DFT with a first group of Twdle factors; the second step calculates 7-point DFT and multiplies with the second group Twdle factor; thirdly, calculating a 3-point DFT; and fourthly, sequentially rearranging output results.
First step as shown in fig. 2, the first step is composed of 21 13-point DFT, input time domain sequences are grouped according to a modulus 21, and divided into 21 groups as inputs of the 13-point DFT, a signal input to the group is subjected to multiplication addition calculation with a first group DFT factor (m = 1) in each group of 13-point DFT, and the calculation result is output as the group of 13-point DFT. The output of each group of 13-point DFT is multiplied by the Twiddle factor (m = 1) of the first group 21 × 13 as the input of the next 21-point DFT, and the condition that the output of the kth group of the first step needs to be satisfied as the kth input of each group of the second step is sorted, for example, in fig. 2, the output of the first group of 13-point DFT (the uppermost one in fig. 2 is the first group) is multiplied by the Twiddle factor of the first group 21 × 13 as the 1 st input of each group of 21-point DFT, the output of the second group of 13-point DFT is multiplied by the Twiddle factor of the first group 21 × 13 as the 2 nd input of each group of 21-point DFT, and so on, the output of the 21 st group of 13-point DFT is multiplied by the Twiddle factor of the first group 21 × 13 as the input of each group of 21-point DFT. The first-step disassembly builds the whole framework of 273-point DFT, and forms a 13 × 21 disassembly structure, i.e. converting 273-point DFT calculation into 13 times of recursive operation of 21-point DFT.
The second step is shown in fig. 3, and similar to the first step, the second step is to perform the decomposition of 21-point DFT of each iteration unit (13 groups of 21-point DFT), and the decomposition is to be a 7 × 3 structure. The output signals of the first step are grouped modulo-3 into 3 groups, where the inputs y (0) to y (20) in fig. 3 are the inputs of each group of 21-point DFT mentioned in the first step in fig. 2, and y (0) to y (20) are divided into three groups as the inputs of each group of 7-point DFT. The output of each group of 7-point DFT is multiplied by the Twiddle factor (m = 2) of the second group 3 × 7 as the input of the third step 3-point DFT, and the condition that the output of the g-th group of the first step is required to be satisfied as the g-th input of each group of the second step is sorted, for example, in fig. 3, the output of the first group 7-point DFT (the first group uppermost in fig. 3) is multiplied by the Twiddle factor of the second group 21 × 13 as the 1 st input of each group of 3-point DFT, the output of the second group 7-point DFT is multiplied by the Twiddle factor of the second group 21 × 13 as the 2 nd input of each group of 7-point DFT, and the output of the third group 7-point DFT is multiplied by the Twiddle factor of the second group 21 × 13 as the input of each group of 7-point DFT. The second step of the process converts the 21-point DFT computation into 7 recursive operations of 3-point DFT.
And thirdly, performing iterative computation on the output result of the second step according to the outer 13 times and the inner 7 times to obtain the result of the whole 273-point DFT.
And the fourth step is sequentially rearranged, the result obtained by the third step cannot be used as the final output, because the DFT splitting is performed twice, the order of the output of the third step is disordered compared with the input of the first step, the two times of splitting are combined for rearranging twice, order adjustment is realized, the order of the sequence output after i times of iteration is adjusted according to the factor set which is well arranged during the prime factor decomposition, the output order of 21-point DFT is disordered and is not sequentially ordered from X (0) to X (272) as can be seen from FIG. 2, and the output order of 3-point DFT is disordered and is not sequentially ordered from Y (0) to Y (20) as can be seen from FIG. 3. As shown in fig. 4, the adjusted outputs are sequentially sorted from X (0) to X (272), and are output as the last output of the 273-point DFT, corresponding to the input order of X (0) to X (272).
It can be seen from the embodiment that, in the aspect of engineering implementation, the whole process is clearly optimized by optimizing the Cooley-Tukey algorithm, and the automatic processing is realized by decomposing prime factors, disassembling N-point DFTs, calculating DFT factors, calculating Twidle factors, calculating calibration compensation and other processes, so that the difficulty in algorithm implementation is greatly simplified; meanwhile, because the automation of partial algorithm flow is realized by adopting a computer, the stability and reliability of the whole algorithm realization are improved; the invention has universality and can be applied to any non-2-base DFT or IDFT.
The above is a further detailed description of the present invention with reference to specific examples, which should not be construed as limiting the specific embodiments of the present invention, but rather as a number of simple deductions or substitutions for those skilled in the art without departing from the spirit of the invention, which should be construed as belonging to the scope of the invention as defined by the appended claims. The previous description of the disclosed embodiments is provided to enable any person skilled in the art to make or use the present application. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other embodiments without departing from the spirit or scope of the application. Thus, the present application is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.
Claims (4)
1. A non-2-base DFT optimized signal processing method is based on Cooley-Tukey algorithm, and is characterized in that: optimizing the prime factor decomposition of the Cooley-Tukey algorithm, disassembling the N-point DFT according to the prime factor decomposition, and processing the signal by using the Cooley-Tukey algorithm on the basis; the quality factor decomposition specifically comprises the following steps: for fixed-point non-2-basis signals of length N, N is prime factorized with N = N 1 ×N 2 ×…×N i In which N is m Are prime numbers and can be repeated, and m belongs to {1,2, \ 8230;, i }; the N-point DFT disassembly specifically comprises the following steps: all N are m In descending order, the sequence is { N' 1 ，N′ 2 ，…，N i '} combining the factors by N' 2 N′ 3 …N i ′×N 1 ′，N′ 3 N′ 4 …N i ′×N′ 2 ，N′ 4 N′ 5 …N i ′×N′ 3 ，…，N i ′×N′ i-1 Divided into i-1 matrices.
2. The non-2-based DFT optimized signal processing method as recited in claim 1, wherein: calculating a DFT factor: based on the N-point DFT, according to the arranged factor set { N } 1 ′，N′ 2 ，…，N i ' } generating DFT factors and scaling the DFT factors; computing Twiddle factor: and on the basis of disassembling the N-point DFT, generating a Twdle factor according to the divided matrix, and calibrating the Twdle factor.
3. The non-2-based DFT optimized signal processing method as recited in claim 2, wherein: further comprising calculating a scaling compensation, combining the factors to { N' 1 ，N′ 2 ，…，N i ' } carrying out calibration backspacing value compensation calculation:
where B is the number of scaled compensation bits and r is the number of scaled integer bits.
4. The non-2-based DFT optimized signal processing method as recited in claim 1,2 or 3, further comprising: the signal processing specifically comprises: (1) For N of m < i m Point DFT, divide the signal into N' m+1 N′ m+2 …×N i ' groups, each group being respectively multiplied and added with the m-th group DFT factors as N m Outputting a point DFT; n' m+1 N′ m+2 …×N i ' group N m The outputs of the point DFTs are multiplied by the m-th group Twdle factors, and the result is N' m+1 N′ m+2 …×N i ' Point DFT input, wherein when m =1, the signal refers to the fixed-point non-2-base signal of the original input, and the rest of the signal refers to N m-1 The result of multiplying the output of the point DFT by the (m-1) th set of Twdle factors; (2) performing step i-1 of step (1); (3) Calculating N i ' Point DFT: is N' i-1 The result of multiplying the point DFT by the corresponding Twdle factor is iterated by N 'from inner layer to outer layer respectively' i-1 ，N′ i-2 ，…N′ 2 Sub-calculation of N i ' Point DFT; (4) To N i The output of the' point DFT is output after being rearranged in order.
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